How much torque does the flywheel exert on the machine


Asked by wiki @ in Physics viewed by 91 People


Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 Kg. Its maximum angular velocity is 12000 rpm.

a) A motor spins up the flywheel with a constant torque of 50 Nm. How long does it take the flywheel to reach top speed?
b) How much energy is stored in the flywheel?
c) The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half of the energy stored in the flywheel is delivered in 2.0 s. What is the average power delivered to the machine?
d) How much torque does the flywheel exert on the machine?

Answered by wiki @



We have that for the Question "Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power" it can be said that

  • \  t=254.03s \\\\
  • E=917.800J\\\\
  • P=229,439.4 W
  • t=2232.05Nm

From the question we are told

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 Kg. Its maximum angular velocity is 12000 rpm.


a) A motor spins up the flywheel with a constant torque of 50 Nm. How long does it take the flywheel to reach top speed?  

b) How much energy is stored in the flywheel?  

c) The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half of the energy stored in the flywheel is delivered in 2.0 s. What is the average power delivered to the machine?  

d) How much torque does the flywheel exert on the machine?


a)

Generally the equation for the acceleration  is mathematically given as

a=\frac{T}{I}\\\\a=\frac{60}{126.563}

a=0.472rads/s^2

t=w/a\\\\t=120.43/0.4741\\\\

\  t=254.03s \\\\

b)

E=\frac{1}{2}iw^2\\\\E=0.5*126.56*120.43^2\\\\

E=917.800J\\\\

c)

P=\frac{917.800}{2}

P=229,439.4 W

d)

a=\frac{dw}{dt}\\\\a=\frac{(120.4-85.2)}{2}\\\\a=17.64\\\\

Therefore

t=I*a

t=126.563*17.64

t=2232.05Nm


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